On A World that has both Legal Slavery and A American style kill in defence on your property law could someone use that defence on your property to kill someone that caught harming 1 of their slaves since slaves are their owners legal property

You can decide what the precedent has been in the past on this planet. There are legal arguments both ways, but in the end it all depends on what the judges (and juries if any) decided in past cases.

You decide if it is legal on this world at that time. If the Players come back in 10 years, it might be different. Interpreting the law is fluid and how a particular law is interpreted changes over time.

On A World that has both Legal Slavery and A American style kill in defence on your property law could someone use that defence on your property to kill someone that caught harming 1 of their slaves since slaves are their owners legal property

A World that has legal slavery probably would not be technologically advanced, as they wouldn't have robots to do the work, if they did have robots, they wouldn't need slaves. So if your in a spaceship and you land on a primitive planet that still has slavery, you just take out your laser rifle and blow them away if the authorities give you any trouble! Since they are likely only to have primitive muskets and the like.

Tech level isn’t really the issue. A government or corporation could have a system where criminals could be put into slavery, or those with debts sign up for a ten year contract to pay them off. Why buy robots when you effectively have a free work force. The main thing I’d say is that as GM, you decide. Even if the law seems odd or “outdated” if you decide the planet has that law, then it has that law. Unless you want to go into the history of the planet and decide just how this is still a thing there, all you can do is present a snapshot of the planet how it is now.